Gate2017 ss Q14

14Let L₁, L₂ be any two context free languages and R be any regular language. Then which of the following is/are CORRECT?
I. L₁ ∪ L₂is context – free
II. L₁ is context – free
III. L₁ - R is context – free
IV. L₁ ∩ L₂ is context – free

Option : B
Explanation :
Given L₁ and L₂ are context free languages and R is a regular language.
I. L₁ ∪ L₂ is context free is CORRECT, context free language are closed under union operation.
II. L₁ is context free is INCORRECT, context free languages are not closed under complement operation.
III. L₁ - R is Context free is CORRECT.
L₁ - R = L₁ ∩ R, Context free intersection Regular is always Context free.
IV. L₁ ∩ L₂ is context free is INCORRECT; context free languages are not closed under complement operation.

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